Question: The sum of two numbers is $64$, and their difference is $40$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 64}$ ${x-y = 40}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 104 $ $ x = \dfrac{104}{2} $ ${x = 52}$ Now that you know ${x = 52}$ , plug it back into $ {x+y = 64}$ to find $y$ ${(52)}{ + y = 64}$ ${y = 12}$ You can also plug ${x = 52}$ into $ {x-y = 40}$ and get the same answer for $y$ ${(52)}{ - y = 40}$ ${y = 12}$ Therefore, the larger number is $52$, and the smaller number is $12$.